`scipy.special._basic:ivp`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:1059

Signature

def ivp(v, z, n = 1)

Summary

Compute derivatives of modified Bessel functions of the first kind.

Extended Summary

Compute the nth derivative of the modified Bessel function Iv with respect to z.

Parameters

v : array_like or float: Order of Bessel function
z : array_like: Argument at which to evaluate the derivative; can be real or complex.
n : int, default 1: Order of derivative. For 0, returns the Bessel function iv itself.

Returns

: scalar or ndarray: nth derivative of the modified Bessel function.

Notes

The derivative is computed using the relation DLFM 10.29.5 ^[2].

Examples

Compute the modified Bessel function of the first kind of order 0 and its first two derivatives at 1.

from scipy.special import ivp

✓

ivp(0, 1, 0), ivp(0, 1, 1), ivp(0, 1, 2)

✗

(np.float64(1.2660658777520084), np.float64(0.565159103992485), np.float64(0.7009067737595233))

Compute the first derivative of the modified Bessel function of the first kind for several orders at 1 by providing an array for `v`.

ivp([0, 1, 2], 1, 1)

✗

array([0.565, 0.701, 0.294])

Compute the first derivative of the modified Bessel function of the first kind of order 0 at several points by providing an array for `z`.

import numpy as np
points = np.array([0., 1.5, 3.])

✓

ivp(0, points, 1)

✗

array([0.   , 0.982, 3.953])

Plot the modified Bessel function of the first kind of order 1 and its first three derivatives.

import matplotlib.pyplot as plt
x = np.linspace(-5, 5, 1000)
fig, ax = plt.subplots()

✓

ax.plot(x, ivp(1, x, 0), label=r"$I_1$")
ax.plot(x, ivp(1, x, 1), label=r"$I_1'$")
ax.plot(x, ivp(1, x, 2), label=r"$I_1''$")
ax.plot(x, ivp(1, x, 3), label=r"$I_1'''$")
plt.legend()

✗

<matplotlib.legend.Legend object at 0x7f3f697317f0>

plt.show()

✓

Aliases

scipy.special.ivp